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Amplitudes for the Exotic b1π Decay (view source)
Revision as of 17:09, 15 August 2011
, 17:09, 15 August 2011→Decay of t-channel resonance X to b1π
<math>
<math>
\langle \Omega_{b_1} 0 \lambda_{b_1} | U_X | J_X m_X \rangle
\langle \Omega_{b_1} \lambda_{b_1} 0| U_X | J_X m_X \rangle
=\sum_{L_X}
=\sum_{L_X}
\left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_{b_1}) \right]
\left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_{b_1}) \right]
<math>
<math>
\langle \Omega_\omega 0 \lambda_\omega | U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle
\langle \Omega_\omega \lambda_\omega 0| U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle
=\sum_{L_{b_1}}
=\sum_{L_{b_1}}
\left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1} \lambda_\omega}^{1 *}(\Omega_\omega) \right]
\left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1} \lambda_\omega}^{1 *}(\Omega_\omega) \right]
<math>
<math>
\langle \Omega_\rho 0 \lambda_\rho | U_\omega | 1 , m_\omega=\lambda_\omega \rangle
\langle \Omega_\rho \lambda_\rho 0| U_\omega | 1 , m_\omega=\lambda_\omega \rangle
=\sum_{L_\omega J_\rho}
=\sum_{L_\omega J_\rho}
\left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega \lambda_\rho}^{1 *}(\Omega_\rho) \right]
\left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega \lambda_\rho}^{1 *}(\Omega_\rho) \right]